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Nonlinear Analysis

Numerical solution of the stationary Gross–Pitaevskii equation: tests of a combined imaginary-time-marching technique with splitting

Maria Mercede Cerimele, Maria Luisa Chiofalo, Francesca Pistella

Published Aug 1, 2001• 5 citations
Publisher
DOI
10.1016/s0362-546x(01)00450-3

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In this paper we present new versions of previously published numerical programs for solving the dipolar Gross–Pitaevskii (GP) equation including the contact interaction in two and three spatial dimensions in imaginary and in real time, yielding both stationary and non-stationary solutions. New versions of programs were developed using CUDA toolkit and can make use of Nvidia GPU devices. The algorithm used is the same split-step semi-implicit Crank–Nicolson method as in the previous version (Kishor Kumar et al., 2015), which is here implemented as a series of CUDA kernels that compute the solution on the GPU. In addition, the Fast Fourier Transform (FFT) library used in the previous version is replaced by cuFFT library, which works on CUDA-enabled GPUs. We present speedup test results obtained using new versions of programs and demonstrate an average speedup of 12–25, depending on the program and input size. The original version of this program (AEWL_v1_0) may be found at dx.doi.org/10.1016/j.cpc.2015.03.024